OFFSET
0,3
COMMENTS
These are "free polyforms" because they are counted up to rotation and reflection.
A bisymmetric hendecahedron is an 11-sided polyhedron that is similar to the convex hull of (-2,1,-1), (-2,1,1), (-1,-1,0), (0,-1,-1), (0,-1,1), (0,0,-2), (0,0,2), (0,2,0), (1,-1,0), (2,1,-1), and (2,1,1).
LINKS
Bert Dobbelaere, Peter Kagey, Drake Thomas, and Andrés R. Vindas-Meléndez, Building with Blocks: Enumerating Polyforms on Tilings, arXiv:2602.23301 [math.CO], 2026. See p. 9.
Wikipedia, Bisymmetric hendecahedron
Jiangmei Wu and Guy Inchbald, Folding Space-Filling Bisymmetric Hendecahedron for a Large-Scale Art Installation, Bridges 2018 Conference Proceedings.
Jiangmei Wu, Synergia (sculpture made from bisymmetric hendecahedra).
EXAMPLE
For n = 2, the a(2) = 4 distinct compounds of two bisymmetric hendecahedra correspond to placing the four distinct types of faces (square, kite, rhombus, and triangle) together.
CROSSREFS
Cf. A038119 (cubic), A038173 (rhombic dodecahedral), A038181 (truncated octahedral), A343909 (tetrahedral-octahedral), A365654 (square bipyramidal), A384254 (rectified cubic), A384274 (quarter cubic), A384754 (omnitruncated cubic), A385024 (tetragonal disphenoidal), A385025 (gyrobifastigium), A385026 (hexagonal prismatic), A385027 (triakis truncated tetrahedral), A385267 (half pyramidille), A385268 (oblate cubille), A385269 (quarter cubille), A385270 (elongated dodecahedral), A385271 (hexakis cubic), A385272 (phyllic disphenoidal), A385273 (quarter oblate octahedrille), A385274 (rhombic pyramidal), A385275 (square quarter pyramidille), A385276 (trapezo-rhombic dodecahedral), A385277 (triangular prismatic), A385278 (triangular pyramidille).
KEYWORD
nonn,hard,more
AUTHOR
Peter Kagey, Aug 13 2025
STATUS
approved